The Governments in DyP: (in general order of appearance)
Anarchy - Default, try and stay out of this as much as possible.
Chiefdom - Early tribal government, not good for large empires. Get out of it as soon as possible to relieve the tile penalty.
Monarchy - This is not your father's Civ3 monarchy. This represents the earliest monarchies of the Egyptian Pharoahs, Mesopotamian Priest-Kings and Emperors of China. It's better than the primitive chiefdom, but don't let the name fool you.
Republic - Meant to represent the Republic of Rome this government is good for raising large armies in preparations for building your early empire.
Democracy - Here we were trying to model the Democracy of Athens, though the limitations of the game make that nearly impossible. In a DyP Democracy youget the tile bonus (this is why the AI loves it) which means your coffers will fill up much faster. It is, however much less suited for waging wars than its cousin the Republic. Units cost more and you get fewer free, in addition there is war weariness to contend with.
Feudal Monarchy - This is what most people will remember as Monarchy. In the FM you are able to support a large army as long as your settlements remain towns or cities.
Fundamentalism - Fundamentalist governments are good for raising large armies, but don't go over your alloted support because each unit above that will cost you. The major drawbacks to the Fundamentalist government are the poor rate cap and the low worker rate.
Theocracy - One of only two governments that do not require maintenance for buildings the Theocracy is ideal for peaceful players who just want to develop their empires without any expansionistic goals. Theocracies recieve very few free units, and have a high war weariness, in addition they have a low rate cap and low worker rate. You should be able to make a lot of money as long as you don't try to field a large army.
Absolute Monarchy - One of the better governments with no real major disadvantages.
Communism - Communal corruption, low war weariness and lots of troops. This one is for the war mongerers.
Fascism - Pretty much the same as Communism but without the communal corruption. The overall corruption level should be nearly the same as under communism.
Constitutional Monarchy - Low corruption, some war weariness and the tile bonus. This is one of the top governments.
Federal Republic - very similar to CM, but with tile bonus, minimal corruption and high war weariness.
Social Democracy - Communal corruption, tile bonus, no improvement maintenance, high war weariness, and few troops. If you have complete control of the planet this is the governement for you.